Gardner Montgomery
03/20/2023 · Junior High School
The surface area \( S \) (in square meters) of a hot-air balloon is given by \( S(r)=4 \pi r^{2} \) where \( r \) is the radius of the balloon (in meters). If the radius \( r \) is increasing with time \( t \) (in seconds) according to the formula \( r(t)=\frac{3}{4} t^{3}, t \geq 0 \), fir the surface area \( S \) of the balloon as a function of the time \( t \). \( S(t)=\square \) (Type an expression using t as the variable. Type an exact answer, using \( \pi \) as needed. Use integers or fractions any numbers in the expression. Simplify your answer.)
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\( S(t) = \frac{9 \pi}{4} t^6 \)
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